Nuprl Lemma : implies-sub_cubical_set
∀[Y,X:j⊢].
(sub_cubical_set{j:l}(Y; X)) supposing
((∀A,B:fset(ℕ). ∀g:B ⟶ A. ∀rho:Y(A). (g(rho) = g(rho) ∈ X(B))) and
(∀I:fset(ℕ). (Y(I) ⊆r X(I))))
Proof
Definitions occuring in Statement :
sub_cubical_set: Y ⊆ X,
cube-set-restriction: f(s),
I_cube: A(I),
cubical_set: CubicalSet,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cube-set-restriction: f(s),
psc-restriction: f(s),
sub_cubical_set: Y ⊆ X,
sub_ps_context: Y ⊆ X,
cube_set_map: A ⟶ B,
csm-id: 1(X),
pscm-id: 1(X)
Lemmas referenced :
implies-sub_ps_context,
cube-cat_wf,
cat_ob_pair_lemma,
cat_arrow_triple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_functionElimination,
Error :memTop
Latex:
\mforall{}[Y,X:j\mvdash{}].
(sub\_cubical\_set\{j:l\}(Y; X)) supposing
((\mforall{}A,B:fset(\mBbbN{}). \mforall{}g:B {}\mrightarrow{} A. \mforall{}rho:Y(A). (g(rho) = g(rho))) and
(\mforall{}I:fset(\mBbbN{}). (Y(I) \msubseteq{}r X(I))))
Date html generated:
2020_05_20-PM-01_43_31
Last ObjectModification:
2020_04_03-PM-04_14_47
Theory : cubical!type!theory
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